There is considerable interest in interrogation and manipulation of surface properties of inorganic and biological materials at molecular level using micro-cantilevers such as an atomic force microscope (AFM). The AFM is often operated in dynamic mode methods (i.e. amplitude modulation and frequency modulation) to image with low lateral force and high force sensitivity. A schematic of AFM operating in dynamic mode is shown in FIG. 1. In this mode of operation a sinusoidal excitation is applied at the base of the cantilever by a dither piezo. The tip of the oscillating cantilever interacts with the sample. The cantilever tip deflection is measured by a photo diode. A set point amplitude of the deflection signal is maintained by feeding back the amplitude signal to the sample positioning system (z-piezo). The sample is raster scanned by XY-scanner. In the amplitude modulation method, the corresponding control signal and the amplitude and phase of cantilever deflection signal during scanning is used to construct the image of the sample. During imaging the effective spring constant and damping coefficient of the cantilever changes due to interaction with the sample. In the frequency modulation method, the frequency of the excitation signal is regulated according to the shift in resonance frequency of the cantilever due to tip-sample interaction during scanning and the frequency shift is used to construct an image.
The scan speed is dictated by the mechanical bandwidth of the sample positioning system and the cantilever. The resolution is high if the quality factor (Q) of the cantilever is high. However due to high quality factor the settling time of the cantilever is high (since the bandwidth of the cantilever is low) and the imaging signals amplitude, phase and the frequency are slow. Therefore the bandwidth of imaging is low.
Recently several methods have been proposed to increase the bandwidth or the resolution of imaging in dynamic mode atomic force microscopy. For example, one method used is that while imaging in air, the scan speed is increased by using a z-piezo with high bandwidth and by active damping (Q-control) of the cantilever. In another method, the force sensitivity (resolution) is enhanced by 3 orders of magnitude by active Q-enhancement of the cantilever. Given a z-piezo with a high mechanical bandwidth the bandwidth and resolution of imaging is dictated by the Q of the cantilever.
There is considerable interest in imaging under fluids with Q-enhancement. Due to the presence of a moisture layer on the sample in air, molecular forces (in piconewton range) are not accessible due to capillary forces (in nanonewton range). However, atomic resolution images have been obtained in water. The samples, e.g., biological samples, are soft and they can be imaged in a buffer solution. The low lateral forces in fluids also favors imaging of biological sample as they are not displaced or destroyed. There are numerous advantages to image under fluids. However, under fluids the quality factor and the force sensitivity of the cantilever are reduced by approximately two orders of magnitude compared to their value in air. Therefore it is essential to actively enhance the Q of cantilever and consequently the force sensitivity in order to sense molecular lever forces and image the soft biological samples.
In the existing methods the deflection signal is phase shifted (or time delayed) and amplified before adding it to the standard excitation signal to control Q. This is based on the assumption that the output is purely sinusoidal and as a result, the phase shifted signal is assumed to provide a true estimate of velocity. However, in this approach, the trade off between bandwidth and resolution remains inherent. In spite of the specific needs, it is always desired to improve both bandwidth and resolution together.